Non-P\'olya Fields with Large P\'olya Groups Arising from Lehmer Quintics
Number Theory
2022-10-25 v1
Abstract
In this article we construct a new family of quintic non-P\'olya fields with large P\'olya groups. We study the upper bound of P\'olya numbers of such fields and show that the P\'olya numbers never exceed five times the size of its P\'olya group. Finally we show that such non-P\'olya fields are non-monogenic fields of field index one.
Cite
@article{arxiv.2210.13102,
title = {Non-P\'olya Fields with Large P\'olya Groups Arising from Lehmer Quintics},
author = {Nimish Kumar Mahapatra and Prem Prakash Pandey},
journal= {arXiv preprint arXiv:2210.13102},
year = {2022}
}
Comments
13 pages